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Large volumes of spatial data and multidimensional data are being published on the Semantic Web, which has led to new opportunities for advanced analysis, such as Spatial Online Analytical Processing (SOLAP). The RDF Data Cube (QB) and…
Space filling curves (SFCs) are widely used in the design of indexes for spatial and temporal data. Clustering is a key metric for an SFC, that measures how well the curve preserves locality in moving from higher dimensions to a single…
Significant research effort has been devoted to improving the performance of join processing in the massively parallel computation model, where the goal is to evaluate a query with the minimum possible data transfer between machines.…
The evolution of programming languages from low-level assembly to high-level abstractions demonstrates a fundamental principle: by constraining how programmers express computation and enriching semantic information at the language level, we…
In this paper, we describe efficient MapReduce simulations of parallel algorithms specified in the BSP and PRAM models. We also provide some applications of these simulation results to problems in parallel computational geometry for the…
We study the algorithmic complexity of embeddings between bi-embeddable equivalence structures. We define the notions of computable bi-embeddable categoricity, (relative) $\Delta^0_\alpha$ bi-embeddable categoricity, and degrees of…
Following the programme set out in Part I of this work, we develop a conceptual higher order differential calculus. The '' local linear algebra '' defined in Part I is generalized by '' higher order local linear algebra ''. The underlying…
Ontology operations, e.g., aligning and merging, were studied and implemented extensively in different settings, such as, categorical operations, relation algebras, typed graph grammars, with different concerns. However, aligning and…
Closure spaces are a generalisation of topological spaces obtained by removing the idempotence requirement on the closure operator. We adapt the standard notion of bisimilarity for topological models, namely Topo-bisimilarity, to closure…
Place-cell networks, typically forced to pairwise synaptic interactions, are widely studied as models of cognitive maps: such models, however, share a severely limited storage capacity, scaling linearly with network size and with a very…
Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…
While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of…
We extend the Theory of Computation on real numbers, continuous real functions, and bounded closed Euclidean subsets, to compact metric spaces $(X,d)$: thereby generically including computational and optimization problems over higher types,…
Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…
A ladder structure of operators is presented for the associated Legendre polynomials and the spherical harmonics showing that both belong to the same irreducible representation of so(3,2). As both are also bases of square-integrable…
Data similarity is a key concept in many data-driven applications. Many algorithms are sensitive to similarity measures. To tackle this fundamental problem, automatically learning of similarity information from data via self-expression has…
We investigate the computational properties of basic mathematical notions pertaining to $\mathbb{R}\rightarrow \mathbb{R}$-functions and subsets of $\mathbb{R}$, like finiteness, countability, (absolute) continuity, bounded variation,…
This paper presents the design and analysis of parallel approximation algorithms for facility-location problems, including $\NC$ and $\RNC$ algorithms for (metric) facility location, $k$-center, $k$-median, and $k$-means. These problems…
The generation and collection of big data series are becoming an integral part of many emerging applications in sciences, IoT, finance, and web applications among several others. The terabyte-scale of data series has motivated recent…
This paper presents Orthogonal Subspace Clustering (OSC), an innovative method for high-dimensional data clustering. We first establish a theoretical theorem proving that high-dimensional data can be decomposed into orthogonal subspaces in…